CSc 343 Computer Organization and Programming
Fall Quarter 1997
Quiz #1 (3 October 1997, Friday) with Solutions

1. Convert the decimal number 153 into binary and hexadecimal notations.

   Binary:      10011001
   
   Hexadecimal: 99
   

2. Express the following bit patterns in hexadecimal notation:

     
     a. 110101101100 
   
             D6C
   
     b. 111100000001
   
             F01
   
   

3. Convert each of the following decimal representations to its equivalent two's complement form using patterns of eight bits:

     
   
     a. -19   
   
        11101101
                      
     b. 28    
   
        00011100
   
   

4. Convert the fractional value to its equivalent floating point notation (using 1 bit for sign, 3 bits for exponent in excess-4 notation, and 4 bits for mantissa). How many different bit-patterns are there for in this notation? List all of them.

   
   Two notations for 7/32:
   
   0 011 0111
   0 010 1110
   
   

5. Suppose a machine stores fractions in floating point notation with 1 bit for sign, 4 bits for exponent and 4 bits for mantissa.
   1. What is the largest number that can be represented in this notation?
      

        +120.0
      

   2. What is the smallest number that can be represented in this notation?
      

        -120.0
      

   3. What is the smallest number in magnitude that can be represented in this notation?
      

        0  (1/4096 is the smallest non-zero number)
      

6. What bit pattern represents the sum of 01101010 and 11001100 if the patterns represent integers represented in two's complement notation ?
   

     00110110
   

7. Convert the following IEEE floating-point number to decimal notation:

      1 10000100 01011100000000000000000
   
      -43.5
   

True or false :

1. The smallest unit of storage inside the computer is a byte. FALSE
2. A machine with a RISC architecture has a larger variety of machine instructions than a machine with a CISC architecture. FALSE
3. Pipelining increases the execution speed of a machine. TRUE
4. In sign-magnitude notation, the value 0 can be represented in more than one way. TRUE
5. The total numbers of integers that can be represented using an 8-bit string in 2's complement notation is 255. FALSE